Telecommunication engineers frequently model telecommunication networks for a variety of purposes. For example, such modeling information can be used to design, properly and effectively, new networks and identify traffic flow problems in existing networks. The networks can then be reconfigured to remove the problems, thereby enhancing dramatically both network performance and the quality of subscriber service. When a customer orders an enterprise system, it is necessary to provide recommendations for the required desired quantities of the various components and resources to be used. Many such components are traffic-sensitive and must be sized based upon anticipated call traffic levels.
Much of the modeling theories and algorithms have been developed for circuit-switched networks. Normally, the usage of a circuit-switched transmission route or switch can be defined by two parameters, namely the calling rate, or the number of times a route or traffic path, is used per unit period (or more properly defined the call intensity per traffic path during the busy hour) and the holding time, or the duration of occupancy of a traffic path by a call (or sometimes the average duration of occupancy of one or more paths by calls). The “busy hour” refers to the carried and/or offered traffic on a traffic path during the busiest continuous one-hour period of a typical day. Carried traffic is the volume of traffic actually carried by a traffic path, and offered traffic is the volume of traffic offered to the traffic path. A traffic path is a channel, time slot, frequency band, line, trunk, link, switch, server, network, circuit, or other network component over which individual communications pass concurrently or in sequence. Traffic density refers to the number of simultaneous calls at a given moment while traffic intensity represents the average traffic density during a one-hour period (and is denoted by the unit Erlang). The grade of service, denoted by p, expresses the probability of meeting call blockage during the busy hour.
When dimensioning a traffic path, several mathematical formulas have been used. The Erlang B loss formula (which is typically based on lost calls cleared) is given by the following mathematical relationship:
      E    B    =                    A        n            /              n        !                    1      +      A      +                        A          2                /                  2          !                    +      …      +                        A          n                /                  n          !                    where EB is the grade of service (i.e., the probability of finding all channels busy) n is the number of trunks or servicing channels, and A is the mean of the offered traffic. The formula assumes that traffic originates from an infinite number of sources, there is equal traffic density per source, lost calls are cleared assuming a zero holding time, the number of trunks or servicing channels are limited, and full availability exists. In the United States, the Poisson or Molina formula is preferred and is given by the following mathematical relationship:
  P  =            e              -        A              ⁢                  ∑                  x          =          n                ∞            ⁢                          ⁢                        A          x                          x          !                    where P is the probability that calls will be lost (or delayed) because of insufficient channels, A is the expected traffic density, expressed in busy hour Erlangs, n is the number of channels in the group of channels, and x is a variable representing a number of busy sources or busy channels. The Poisson formula assumes that traffic originates from a large (infinite) number of independent subscribers or sources (random traffic input) with a limited number of trunks or servicing channels, there is equal traffic density per source, and lost calls are held. Other mathematical formulas in use include the Erlang C formula (which assumes infinite sources, lost calls delayed, exponential holding times, and calls serviced in order of arrival) and the binomial formula (which assumes finite sources, equal traffic density per source, and holding of lost calls).
Network design in general and resource provisioning in particular is becoming increasingly more difficult. The complexity results from the multiplicity of communication modalities, such as circuit-switched voice, packet-switched voice or VoIP, instant messaging, and chat sessions, the differing types of traffic (voice and nonvoice) being handled simultaneously by a packet-switched network and the difficulty in predicting with accuracy the volume and nature of the traffic, the concurrent usage of both circuit-switched and packet-switched networks, the use of encrypted and unencrypted data streams, and the variety and number of software and hardware components required to operate the networks.
Design based on mathematical calculations, such as those noted above, is overwhelming due to the inability to cope with complex network topologies, intricate inter-population calling patterns, and the various influences of compression and resource usages imposed by inter- and intra-site codecs (or coders/decoders). Current mathematical models are capable of dealing with only a few sites, only the most generic calling patterns, and only a grossly simplified application of codecs. Real world examples, however, can include hundreds of sites with unlimited combinations of populations, calling patterns and codecs. These real-world examples are completely beyond the capabilities of any purely mathematical analysis.
Due to the limitations of mathematical approaches, stochastic or event-driven modeling or simulation techniques have been developed to assist in network design. In such techniques, the network is characterized functionally in software and calls having predefined durations are generated at selected intervals. The call interarrival and holding times follow a defined type of probability distribution, such as an exponential distribution. The generated calls are inputted into the logical characterization of the network. The individual call flows through the various nodes of the simulated network can be observed and analyzed. This approach can not only be computationally demanding but also difficult to implement. More complex networks can require hundreds of man hours to logically characterize. Such man-hour expenditures are economically prohibitive in many applications, such as resource provisioning.